We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the quasi-crystalline phasonic degrees of freedom. We show that due to this continuous symmetry, the model undergoes a topological phase transition at a finite temperature, despite the discrete nature of the tiles. We study both the high and low temperature phases, and argue that some of the results are universal properties of 2D systems whose ground state is a quasi-crystalline state.